Solve for $x$ and $y$ by deriving an expression for $x$ from the second equation, and substituting it back into the first equation. $\begin{align*}3x+2y &= 4 \\ -8x+2y &= 2\end{align*}$
Solution: Begin by moving the $y$ -term in the second equation to the right side of the equation. $-8x = -2y+2$ Divide both sides by $-8$ to isolate $x$ $x = {\dfrac{1}{4}y - \dfrac{1}{4}}$ Substitute this expression for $x$ in the first equation. $3({\dfrac{1}{4}y - \dfrac{1}{4}}) + 2y = 4$ $\dfrac{3}{4}y - \dfrac{3}{4} + 2y = 4$ Simplify by combining terms, then solve for $y$ $\dfrac{11}{4}y - \dfrac{3}{4} = 4$ $\dfrac{11}{4}y = \dfrac{19}{4}$ $y = \dfrac{19}{11}$ Substitute $\dfrac{19}{11}$ for $y$ in the top equation. $3x+2( \dfrac{19}{11}) = 4$ $3x+\dfrac{38}{11} = 4$ $3x = \dfrac{6}{11}$ $x = \dfrac{2}{11}$ The solution is $\enspace x = \dfrac{2}{11}, \enspace y = \dfrac{19}{11}$.